Until recently, neither solutions nor connection formulae for Heun Equation and its cousins were known in closed form. As a consequence the most efficient approach to the solution with prescribed boundary conditions (needed e.g. for QNMs) was based on numerical methods developed by Leaver [1]}, relying on continuous fractions that allow to solve (numerically) 3-term recursion relations. When these involve more than 3 terms, Gaussian elimination may be employed to subsequently reduce the number of terms [2]}. A relatively good estimate is provided by the WKB approximation that connects with geodesic motion in the eikonal limit (for large \(\ell \) ) that can be used as a `seed' for numerics.
